diagRevLexInit -- Diagonal initial ideal of an ASM ideal with respect to revlex, ordering variables from NW corner

Synopsis

Usage:

diagRevLexInit w

diagRevLexInit A
Inputs:
- w, a list, or A is a Matrix
Optional inputs:
- CoefficientRing => a ring, default value QQ
- Variable => a symbol, default value z
Outputs:
- a monomial ideal,

Description

Given a partial alternating sign matrix or a permutation in 1-line notation, return the diagonal initial ideal of the corresponding ASM ideal or Schubert determinantal ideal with respect to reverse lexicographic order, where the variables are ordered smallest to largest by reading from rows left-to-right and ordering rows from bottom-to-top (starting in the southwest corner).

This function computes over the coefficient field of rational numbers unless an alternative is specified.

i1 : diagRevLexInit({1,3,2},CoefficientRing=>ZZ/3001)

o1 = monomialIdeal(z   z   )
                    1,1 2,2

o1 : MonomialIdeal of QQ[z   , z   , z   , z   , z   , z   , z   , z   , z   ]
                          1,3   1,2   1,1   2,3   2,2   2,1   3,3   3,2   3,1

i2 : diagRevLexInit(matrix{{0,0,0,1},{0,1,0,0},{1,-1,1,0},{0,1,0,0}})

o2 = monomialIdeal (z   , z   , z   , z   , z   z   )
                     1,3   1,2   1,1   2,1   2,2 3,1

o2 : MonomialIdeal of QQ[z   , z   , z   , z   , z   , z   , z   , z   , z   , z   , z   , z   , z   , z   , z   , z   ]
                          1,4   1,3   1,2   1,1   2,4   2,3   2,2   2,1   3,4   3,3   3,2   3,1   4,4   4,3   4,2   4,1

Ways to use diagRevLexInit :

diagRevLexInit(List)
diagRevLexInit(Matrix)

For the programmer

The object diagRevLexInit is a method function with options.